My dog Honey is a Jack Russell Shitzu-Hybrid (almost 2 yrs old) always eats grass when we go for a walk.

This behavior she's had since she's a puppy. I was told they eat it when they have worms or indigestion. But she has no worms.

She has a sensitive stomach, because sometimes she vomits also.
She gets wet food to eat-but doesn't have much... maybe a bowl, sometimes two. She weighs 6-7 kg.

She doesn't tolerate the car or train, and will vomit.

How can it be that she is so sensitive? And why does she always need grass?

Even cats eat grass, it's totally fine. It's an additional source of vitamins. Have you tried natural or holistic foods? That might help her sensitive stomach. As to vomitting in the car or train, it looks more like a behaviour problem to me, probably because of fear. Does she display any signs of fear before or when she is having a car (train) ride?

I have a cow at home too! But I also heard it's fine, cats do it so why can't dogs?
So almost every dog I know, eats grass and does not really have any worms.
What many dogs do when they have eaten grass is puke, but according to the vet is not abnormal.
Where you have to watch is the coarse grass, because the dogs can quickly cut their throats with it when swallowing. Have been surprised at Casper that he had blood in the vomit, but it was from the coarse grass he ate, the vet said.
My dog does that too, it's normal Emotion: smile)